what is the unit rate for the ratio 100 points/ 4 games?

Answer:

1. infinite

2. no

3. one

4.no

The number of points of intersection for the graphs of the equations is infinite.

Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.

Simplifying the given equations:

i) x/2 + 5y = 6

x + 10y = 12

ii) 3x + 30y = 36

3(x + 10y) = 36

x + 10y = 12

As the equations are equal lines, they will intersect at infinite times.

Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many

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Answer:

Step-by-step explanation:

men = 2x

women = 3x

2x+3x=135

5x=135

x=27

27(2)=men

54 men

Hence,  when [tex]n=10[/tex] the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality [tex]2(n + 2) < 5(n -1)[/tex] true.

So,

[tex]2(n + 2) < 5(n-1)[/tex]

When

[tex]n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45[/tex]

Hence,  when [tex]n=10[/tex] the given inequality is true.

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Answer:

The answer is in the image I attached to this response. Let p = the cost of 1 pencil, and let r = the cost of 1 ruler.

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(A)  The probability that, after 11 weeks, the supply of gasoline will be below 20000 gallons is 0.2643.

(B) 52854.8 gallons should be the weekly delivery so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%.

Given,

u = 50000

s = 10000

n = 11

Starting supply = 74000

Weekly delivery = 47000

Total supply for 11-week = 74000 + 11*47000

                                        = 591000

(A) If more than 20,000 gallons of gasoline are purchased overall in these 11 weeks, the supply will fall below that amount.

591000 - 20000 = 571000

We need to find, P(T > 571000) = P(z > [tex]\frac{571000-11(50000)}{\sqrt{1110000} }[/tex])

                                                    = P(z > 0.63)

                                                    = 1 - 0.7357

                                                    = 0.2643

(B) Unknown schedule delivery = A

     Total gasoline should be more than = 74000 + 11*A - 20000

     Probability = 05%

    z-value corresponding it = 2.575

    P(T > 74000 + 11*A - 20000) = 0.05

    [tex]\frac{74000+11A-20000-11(50000)}{\sqrt{1110000} } = 2.575[/tex]

                                        A = 52854.8

Hence, 52854.8 gallons should be the weekly delivery be so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%.

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As per the sampling, an appropriate test value for a z test is 0.808

Sampling:

In math, sampling means selecting the group that you will actually collect data from in your research.

Given,

In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. the bookstore believes that the two groups spent the same amount.

Here we need to find the appropriate test value for a z test.

As per the given question, first we must know the definition of z test,

The term z-test means statistical test that can be used to determine whether two population means are different.

And it is used when the variances are known or the sample size is large.

And the formula of the z value, the test statistic for two population with large sample size is given by,

z = [x₂ - x₁] / √[(s₁²/n₁) + (s₂²/n₂)]

From the question we have, x1=$320, x2=$310, s1=$62, s2=$73, n1=60 and n2 = 60.

When we apply the value then we get the z value as

=> z = [310 - 320] / √[(62²/60) + (73²/60)]

=> 0.808

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Answer: E

Step-by-step explanation:

The measure of ∠WRS is 25°.

What is meaning of intersect point?

A graph intersection is a location where two or more graphs meet. It is a point that is the answer to an equational system. The intersection of two curves is the sole application of the TI series.

Given the points on a line are T, R, W.

The points on another line are V, R, S.

Both lines intersect at R.

Then another line that extends from point R to point Z between ∠VRW.

The angle ∠VRT is 5x° and the angle ∠TRS is (25x + 30)°.

∠VRS is a linear angle means ∠VRS = 180°.

Again,

∠VRS = ∠VRT + ∠TRS

Putting the value of ∠VRS, ∠VRT, ∠TRS

180° =  5x° + (25x + 30)°

180 =  30x + 30

Subtract 30 from both sides:

150 = 30x

Divide both sides by 30:

x = 5.

∠WRS is vertically opposite angle of ∠VRT.

Therefore ∠WRS = ∠VRT = 5x° = (5×5)° = 25°

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(a) 10⁴ strings of four digits which end with an even digit.

(b) 10⁵ strings of four digits which begin with an odd digit.

(a)There are 10 choices ranging from 0 to 1,2...9 for the first three digits of the string that ends in an even number and four possibilities ranging from 2,4,6,8, for the last digit.

According to the product rule there are 4000 strings that terminate in an odd number or 10 × 10 × 10 × 4.

(b) Also there are 10 choices ranging from 0 to 9 for the last three digits of the string that ends in an odd or even number and 5 possibilities ranging from 1,3,5,7,9 for the first digit .

According to the product rule there are 5000 strings that terminates in an even number or 10 × 10 × 10 × 5.

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Answer:

  see the attachment

Step-by-step explanation:

You want graphs of f(x -5) and f(x)+2 and their asymptotes, given exponential function f(x).

The subtraction of 5 from the argument x causes the graph to be shifted to the right 5 units. The horizontal asymptote at y=0 is unchanged.

The addition of 2 to every function value causes the graph to be shifted up 2 units. The horizontal asymptote is likewise shifted up 2 units to y=2.

The red and blue graphs are attached. The asymptotes are dashed lines.

Answer:

1.478 kg

Step-by-step explanation:

Considering density=mass/volume, when we rearrange, we get mass=density*volume. Therefore, as we are given the density, we just need to find the volume to know the mass. The volume of a cylinder is πhr^2, and our radius is 28/2=14, so the volume of the cylinder is π*3*14^2=588π. Then, 588π*0.8=470.4π which is about 1477.8052 g. Then, to convert to kg, we can divide this by 1000 and get about 1.478 kg.

Answer:

d ≥ −11

Step-by-step explanation:

Step 1: Add 5 to both sides.

−2d−5+5 ≤ 17+5

−2d ≤ 22

Step 2: Divide both sides by -2.

−2d/−2 ≤ 22/−2

d ≥ −11

After 3 hours Dylan and Sam will be exactly 15 miles apart .

In the question ,

it is given that ,

the speed at which Dylan is jogging in east = 4 miles per hour .

the speed at which Sam is jogging in south = 3 miles per hour .

the distance covered by Dylan is = 4t

the distance covered by Sam is = 3t

we have to find the time when they are 15 miles apart .

Since Dylan walks in east and Sam walks in South  , it forms a right triangle , so , it will satisfy the Pythagoras Theorem ,

(3t)² + (4t)² = 15²

9t² + 16t² = 225

225 = 25t²

t² = 225/25 = 9

t = 3

Therefore , the time taken will be 3 hours .

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Answer:

Step-by-step explanation:

40/20= 20

39/x=x

that woudl be how you would find it

Answer:

C

Step-by-step explanation:

3y+3=3y-3

taking the 3y from the right to the left and the 3 in the left to the right

3y-3y= -3-3

0=-6

taking the 3y from the left to the right and the 3 in the right to the left

3+3=3y-3y

6=0

Equation to determine the diver’s initial depth is [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable.

The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.

Let the distance of diver at a certain depth be x.

After some time he ascends [tex]10\frac{3}{4}[/tex] feet.

The final position of diver is : [tex]56\frac{1}{2}[/tex] feet.

Using given information we get the required equation: [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].

where x = distance of diver at a certain depth.

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The rewritten summation is [tex]\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)[/tex].

A recursive function is a function that calculates subsequent terms by repeating or using its own prior terms, creating a succession of terms. By definition, the recursive function can be used to write the summation by separating the final term of the summation and adding a final term to the summation.

Given, the function is [tex]\sum_{m=1}^{n+1}m(m+1)[/tex].

First, we have to separate the final term from the given summation. The final term is m = n+1 which is present above the summation. For this replace the n+1 with n.

Then, add the term m(m+1) with m in the given summation replaced by n+1.

The new summation is rewritten as,

[tex]\begin{aligned}\sum_{m=1}^{n+1}&=\sum_{m=1}^{n}m(m+1)+(n+1)((n+1)+1)\\&=\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)\end{aligned}[/tex]

The new summation is rewritten.

The complete question is -

Rewrite by separating off the final term [tex]\sum_{m=1}^{n+1}m(m+1)[/tex]

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The expanded and simplified form of the given expression is [tex]12a^4b^8-18a^3b^3[/tex]. This expansion represents the distributive property.

In this property, the arithmetic operation is as follows:

x(y+z) = xy+xz

Here the term outside of the brackets is multiplied by each term in the brackets.

The given expression is [tex]6a^2b^3(2a^2b^5-3a)[/tex].

It is expanded by using distributive property,

x(y+z) = xy+xz

Here in the expression, [tex]6a^2b^3(2a^2b^5-3a)[/tex] the term 6a²b³ is multiplied by each term in the brackets. So, we get the expanded term.

I.e.,

6a²b³(2a²b⁵- 3a) = (6)(2)(a²)(a²)(b³)(b⁵) - (6)(3)(a²)(a)(b³)

⇒ 6a²b³(2a²b⁵- 3a) = 12a⁴b⁸ - 18a³b³

Here the like terms when multiplied, their powers should be added.

(∵ [tex]x^m\times x^n = x^{m+n}[/tex])

And there is no further simplification for this expanded form since the variables have different powers.

Therefore, the expanded and the simplified form of the given expression is [tex]12a^4b^8-18a^3b^3[/tex].

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The point (11,11) will lie on the graph of the function f(x) = IxI

What is coordinate?

The x-coordinate informs us of a point's separation from the y-axis, which is the vertical axis. The abscissa is another term for the x-coordinate. The y-coordinate shows how far a point is from the horizontal axis, or x-axis. The term "ordinate" also applies to the y-coordinate.

the function: f(x) = IxI

The function will have every positive and negative integer contained within itself.

So coordinates of another point with the same y value (11,11) will lies on the graph so as (-11,11).

Hence point (11,11) will lie on the graph of the function f(x) = IxI

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MCN= ACN-ACN-1 is the basis of diminishing marginal utility.

What is marginal utility?

The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility. Economists utilize the idea of marginal utility to estimate the quantity of a good that consumers will buy.

When the overall utility is increased by the consumption of an additional item, positive marginal utility occurs. On the other side, negative marginal utility arises when the overall utility is reduced by the consumption of one extra unit.

According to the law of diminishing marginal utility, as consumption rises, the marginal utility gained from each additional unit decreases, all other things being equal. The incremental improvement in utility brought on by consuming one more unit is known as marginal utility. An economic term for happiness or contentment is "utility."

So

MCN= ACN-ACN-1

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On solving the provided question we got to know that, favorable cases for X4 to be the least  is that = 0.25

Probabilities are mathematical justifications of the probability that an event will happen or that a proposition is true. A number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty, denotes the likelihood of an event.

[tex]X1, \\X2, \\X3[/tex]

can be arranged in 3! Ways so, in tottal  6 ways

[tex]Hence, there are 6 cases where X4 is the lowest.[/tex]

Total no. of cases on which [tex]X1, X2, X3, X4[/tex] be  arranged are  4! = 24

Favorable cases for [tex]X4[/tex] to be  the least = [tex]6/24 = 1/4 = 0.25[/tex]

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Tests are frequently used to initially determine and assess potential worker safety and health issues.

The following factors are essential to a good workplace safety and health program: Leadership and management commitment. Accountability. Concern for safety.

An idea or rule that directs behaviors, processes, or tools with the goal of reducing the possibility or incidence of harm to people, property, or the environment.

In order to protect people's bodily, mental, and material health as well as the community's overall wellbeing, safety is the condition in which risks and circumstances that could cause harm are under control. It is a necessity for daily existence and is required by both individuals and communities in order to realize their objectives.

Workplace safety procedures are established practices that describe how to carry out duties with the least amount of danger to people, property, and working conditions. The processes cover work-related duties that deal with safety issues, safety gear, and work-area safety precautions.

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The work required to stretch the spring is 91.6 Ibs-inch

What is work?

Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.

Δx : displacement from equilibrium position

f = k Δ x (force due to spring = -kΔx)

where, k is the spring constant

Given,

f = 20ibs

Δx = 24 -18 Inches = 6 inches

∴ k = 20/6 ibs/inch

Now, PE stored in spring = 1/2 k (Δx)²

Δx : displacement from equilibrium position

Work done = change in PE

= 1/2K (Δx₂)² -1/2k (Δx₁)²

given,

Δx₁ = 21-18 inches = 3 inches

Δx₂ = 26-18 inches = 8 inches

∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches

=10/6 *5*11

work done = 91.6 ibs-inch

The spring must be stretched with 91.6 Ibs-inch of force.

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Answer: C - I agree

D - Square root 50 lies between integers 7 and 8

E - Find the closest integer to 40

Step-by-step explanation: C - 7/9 will be 0.77777778 which you can simplify to 0.777

D - The square root of 50 is 7.07106781187 so it is between the integers 7 and

E - The square root of 40 is 6.32455532034 which so find the clossest integer to 40

Emma is asking an empirical question so that she she can test her hypothesis

What is a Empirical hypothesis?

Something empirical is something based on real evidence .

Evidence that is verifiable by observation as opposed to something that is true in theory or by some kind of reckoning or logic

A hypothesis is a theory that is put forward for further examination to see if it is correct. It is not a call but it is an explanation that fits the available evidence so , An empirical hypothesis is a theory that is based on real evidence and experience but that has not been proven yet

So, According to the question

Emma wants to know if long distance relationship in college have a greater likelihood of ending than a relationship that are not long distance and for that she creates a questionnaire and the crowds 100 student from our school to complete the questionnaire so she can test her hypothesis

Here, Emma is asking an empirical questions ( question about experience) and will conclude the test based on these 100 students experience and thoughts.

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Answer:

sum = 196

Step-by-step explanation:

the sum to n terms of an arithmetic series, when the first and last terms are known is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first term + last term)

we require to find the number of terms in the series

the nth term of an arithmetic series is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = a₂ - a₁ = 3 - 1 = 2 , then

1 + 2(n - 1) = 27 ( subtract 1 from both sides )

2(n - 1) = 26 ( divide both sides by 2 )

n - 1 = 13 ( add 1 to both sides )

n = 14 ← number of terms in the series

Then

S₁₄ = [tex]\frac{14}{2}[/tex] (1 + 27) = 7 × 28 = 196

The rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].

What is a rationalized expression?

A rationalized expression is an expression that has been written in a simplified form which eliminates any radicals (square roots, cube roots, etc.) from the denominator. The denominator is made a rational number, meaning it can be expressed as a fraction with an integer numerator and denominator. This is done by multiplying both the numerator and the denominator by the radical of the denominator. This process is called rationalization.

The given expression is

                          [tex]=\frac{\sqrt{9}}{\sqrt{3}+ \sqrt{x} } \\\\=\frac{\sqrt{9} }{\sqrt{3} }+ \frac{\sqrt{9} }{\sqrt{x}}\\\\=\frac{3 }{\sqrt{3} }+\frac{\sqrt{9} }{\sqrt{x}}\\\\=\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex]

Hence, the rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].

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